Method and system for non-invasive assessment of coronary artery disease

ABSTRACT

In order to assess coronary artery disease from medical image data, an anatomical model of a coronary artery is generated from the medical image data. A velocity of blood in the coronary artery is estimated based on a spatio-temporal representation of contrast agent propagation in the medical image data. Blood flow is simulated in the anatomical model of the coronary artery using a computational fluid dynamics (CFD) simulation using the estimated velocity of the blood in the coronary artery as a boundary condition.

This application is a divisional of U.S. patent application Ser. No.13/226,779, filed Sep. 7, 2011, which claims the benefit of U.S.Provisional Application No. 61/383,478, filed Sep. 16, 2010 and U.S.Provisional Application No. 61/384,382, filed Sep. 20, 2010, thedisclosures of which are herein incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates to modeling the cardiovascular circulationusing medical images, and more particularly, to non-invasivepatient-specific assessment of coronary artery disease based on 4Dmedical image data and numerical simulations.

Cardiac disease is the leading cause of death for men and women in theUnited States and accounts no less than 30% of deaths worldwide.Although medical advances in recent years have provided importantimprovements in the diagnosis and treatment of complex cardiac diseases,the incidence of premature morbidity and mortality is still large. Onereason for this is a lack of accurate in-vivo and in-vitro estimates ofpatient-specific parameters that accurately characterize the anatomy,physiology, and hemodynamics, all of which play an important role in theprogression of cardiovascular diseases.

Medical imaging based techniques (e.g., computed tomography (CT),angiography, etc.) are typically used in clinical practice forcharacterizing the severity of stenosis in the coronary arteries.However, such techniques only provide an anatomical assessment, which isoften inadequate for clinical decision making. In particular, anatomicalassessment of the severity of coronary artery stenosis often leads tooverestimation or underestimation, both of which are undesirable.Overestimation of stenosis severity can lead to unnecessary interventionand subsequent risk of restenosis, while underestimation will likelylead to non-treatment. An accurate functional assessment may requiremeasurements of pressure and/or flow, which are determined invasively.

BRIEF SUMMARY OF THE INVENTION

The present invention provides a method and system for non-invasivepatient-specific assessment of coronary artery disease based on 4Dmedical image data. In particular, embodiments of the present inventionprovide flow and pressure measurements using a non-invasiveComputational Fluid Dynamics (CFD) based method that usespatient-specific boundary conditions derived from 4D medical image data.Embodiments of the present invention also provide a non-invasive methodfor measuring the coronary flow reserve (CFR) of a patient based on 4Dmedical image data.

In one embodiment of the present invention, an anatomical model of acoronary artery is generated from medical image data. A velocity ofblood in the coronary artery is estimated based on a spatio-temporalrepresentation of contrast agent propagation in the medical image data.Blood flow is then simulated in the anatomical model of the coronaryartery using a computational fluid dynamics (CFD) simulation using theestimated velocity of the blood in the coronary artery as a boundarycondition.

In another embodiment of the present invention, a first sequence ofmedical image data acquired during rest and a second sequence of medicalimage data acquired during hyperemia are received. A first anatomicalmodel of a coronary artery is generated from the first sequence ofmedical image data and a second anatomical model of the coronary arteryis generated from the second sequence of medical image data. Maximumvelocity of blood in the coronary artery during the resting state isestimated based on a spatio-temporal representation of contrast agentpropagation in the first sequence of medical image data and a maximalhyperemia velocity of blood in the coronary artery is estimated based ona spatio-temporal representation of contrast agent propagation in thefirst sequence of medical image data. To determine the blood flow rates,the maximum velocity during resting state is mapped to an averagevelocity during resting state and the maximum velocity at hyperemia ismapped to an average velocity at hyperemia. The coronary flow reservefor the coronary artery is calculated based on the resting flow rate andthe flow rate during hyperemia.

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a method for patient-specific assessment of coronaryartery disease according to an embodiment of the present invention;

FIG. 2 illustrates exemplary results of the steps of the method of FIG.1;

FIGS. 3A and 3B illustrate velocity estimation based on aspatio-temporal representation of contrast agent propagation accordingto an embodiment of the present invention;

FIG. 4 illustrates a method of non-invasive assessment of coronary flowreserve based on medical image data according to an embodiment of thepresent invention;

FIG. 5 illustrates determination of flow rate in a vessel from avelocity profile of the blood in the vessel; and

FIG. 6 is a high-level block diagram of a computer capable ofimplementing the present invention.

DETAILED DESCRIPTION

The present invention relates to non-invasive assessment of coronaryartery disease using patient-specific modeling of the heart from asequence of volumetric data, such as computed tomography (CT), magneticresonance imaging (MRI), and echocardiography data. Such sequences ofvolumetric data, also referred to herein as 4D image data or 4D images,are sequences taken over a period of time to cover one or more cardiaccycles, in which each frame is a 3D image (volume). Embodiments of thepresent invention are described herein to give a visual understanding ofthe coronary artery disease assessment method. A digital image is oftencomposed of digital representations of one or more objects (or shapes).The digital representation of an object is often described herein interms of identifying and manipulating the objects. Such manipulationsare virtual manipulations accomplished in the memory or othercircuitry/hardware of a computer system. Accordingly, is to beunderstood that embodiments of the present invention may be performedwithin a computer system using data stored within the computer system.

CFD techniques based analysis for functional assessment of coronarydiseases are typically based on simplified geometries of the coronary,with generic boundary conditions derived from population-wide data. Thismakes such techniques unsuitable for a comprehensive patient-specificassessment of a coronary artery disease, such as an assessment ofstenosis severity in the case of coronary artery stenosis. However, inan embodiment of the present invention, a non-invasive CFD-based methoduses patient-specific boundary conditions for both the flow andgeometry, derived from medical image data, such as high resolution CTdata.

Embodiments of the present invention provide a method and system fornon-invasive functional coronary artery disease assessment based on 4Dmedical image data, such as high-resolution CT data, coupled with anunderlying patient-specific hemodynamic analysis using computationalfluid dynamics (CFD) modeling and simulations. In order for theunderlying hemodynamic analysis to generate patient-specific parametersto be used for functional assessment, a 4D (3d+time) patient-specificgeometric model for the coronary arteries of interest is determined fromthe medical image data. An image based analysis of the propagation of acontrast agent, via a spatio-temporal representation of contrast agentpropagation, is performed to robustly recover the velocity profile overtime on the coronary artery of interest. Patient-specific CFDsimulations are performed in the coronary artery of interest, with inletboundary conditions determined by the velocity profile derived from thecontrast agent propagation, and hemodynamic parameters are derived fromthe CFD simulations to characterize the degree of stenosis.

FIG. 1 illustrates a method for patient-specific assessment of coronaryartery disease according to an embodiment of the present invention. Themethod of FIG. 1 transforms image data representing a coronary region ofa patient into a patient-specific anatomical model of the coronaryarteries and uses the patient-specific coronary artery model to simulateblood flow in the coronary arteries the heart.

Referring to FIG. 1, at step 102, medical image data is received. Inparticular, at least one sequence of image data is received. Thesequence of image data can be a sequence of 3D images (volumes) acquiredover a certain time period. For example, such 4D image data (3D+time)can be acquired over a one full heart cycle. One or more sequences ofimage data can be received using various medical imaging modalities. Forexample, according to various embodiments of the present invention, asequence of 3D CT data, 2D dynamic angiography data, and/or rotationalangiography data can be received, but the present invention is notlimited thereto. The image data can be received directly from one ormore image acquisition devices, such as a CT scanner or an X-ray device.It is also possible that previously stored image data be loaded, forexample from a memory or storage of a computer system or some othercomputer readable storage medium. The sequence of medical images canshow the propagation of a contrast agent through the coronary arteries.FIG. 2 illustrates exemplary results of the steps of the method ofFIG. 1. As illustrated in FIG. 2, image 202 shows frames of a highresolution CT volume.

Returning to FIG. 1, at step 104, a patient-specific anatomical model ofthe coronary arteries is generated from the received medical image data.The patient-specific anatomical model is a 4D (3D+time) geometric modelof the coronary arteries generated using the 4D medical image data. Inorder to generate the patient-specific anatomical model of the coronaryarteries, coronary arteries of interest are segmented in each frame ofthe 4D image data. The coronary arteries of interest can be segmented ineach frame using any coronary artery segmentation method. For example,the coronary arteries of interest can be segmented in CT volume usingthe method described United States Published Patent Application No.2010/0067760, which is incorporated herein by reference. A geometricsurface model is then generated for the segmented coronary arteries ofinterest in each frame. For example, methods for anatomical modeling ofthe coronary arteries are described in U.S. Pat. Nos. 7,860,290 and U.S.Pat. No. 7,953,266, both of which are incorporated herein by reference.This results in an anatomical model of the coronary arteries of interestthat shows the anatomy of the coronary arteries changing over time. Asshown in FIG. 2, image 204 shows the coronary artery segmentation andimage 206 show the anatomical modeling of the coronary artery, resultingin a 3D anatomical model.

Returning to FIG. 1, at step 106 the velocity of the blood flow in thecoronary arteries is estimated based on contrast agent propagation inthe received medical image data. In particular, once the coronary treesegmentation has been generated, a spatio-temporal representation ofcontrast agent propagation is derived from time-intensity curves of thereceived medical image data. The spatio-temporal representation of thecontrast agent propagation is used to recover the velocity profile overtime on the coronary of interest.

Spatio-temporal analysis of contrast propagation enables robustestimation of velocity profiles by integrating the availablemeasurements of the intensity profile. FIGS. 3A and 3B illustratevelocity estimation based on a spatio-temporal representation ofcontrast agent propagation according to an embodiment of the presentinvention. As illustrated in FIGS. 3A and 3B, image 300 showtime-intensity curves for input 2D fluoroscopy images. Thetime-intensity curves of image 300 show the inverted intensity magnitudefor points in the 2D fluoroscopy images over the length of a vessel overtime. This information provides a spatio-temporal representation of thecontrast agent propagation, as shown in image 310. A slope 312 isestimated for the spatio-temporal representation of the contrast agentpropagation, and this slope 312 is a first order approximation of thevelocity of the blood in the vessel. This approximation of the velocitycan then be used to set the boundary conditions for the subsequent CFDmodeling. Such an approximation of the velocity in a vessel can beperformed for all coronary arteries of interest, resulting in anestimated velocity profile for the coronary arteries of interest. Asshown in FIG. 2, images 208 and 210 show the spatio-temporal analysis ofcontrast propagation, which is used to generate the time-indexedvelocity profile, resulting in a velocity boundary condition for the CFDmodeling.

Returning to FIG. 1, at step 108, blood flow is simulated in thecoronary arteries using CFD with patient-specific boundary conditions.In particular, the CFD modeling uses the coronary flow velocity profileestimated from the contrast agent propagation to set up boundaryconditions for the CFD modeling. Blood is modeled as a Newtonian fluid,and the velocity field is obtained by numerically solving thediscretized Navier-Stokes equations (continuity and momentum equations)under the rigid wall assumption. The discretized Navier-Stokes equationsare used to incrementally simulate velocity of blood flow and pressurewithin the coronary arteries over time. The patient-specific anatomy ofthe coronary arteries are also input to the CFD modeling in order toconstrain the blood flow simulations based on the patient-specificanatomy.

Several hemodynamic parameters have been proposed for functionalassessment of coronary artery disease, such as flow rates and pressuredrops for assessing the severity and stenosis, and wall-shear stress forplaque formations. However, such parameters were previously calculatedbased on simplified geometries of the coronary, with boundary conditionsderived from population-wide data. According to an advantageousembodiment of the present invention, medical image data, such as highresolution CT data, is used not only to provide the anatomic model, butalso to estimate patient specific boundary conditions for extractingthese hemodynamic parameters via CFD simulations, and using theseparameters for functional assessment of coronary artery disease. Asshown in FIG. 2, image 210 shows the CFD-based hemodynamic analysis.

Returning to FIG. 1, at step 110, patient-specific hemodynamicparameters are output. The patient-specific hemodynamic parameters arecalculated based on the CFD simulations. In particular, the CFDsimulations result in simulated values for pressure and velocity ofblood flow through the coronary arteries over time. These simulatedvalues can be used to calculate various hemodynamic parameters, whichcan be used to assess coronary artery disease. For example, flow ratesand pressure drops can be used for assessing the severity and stenosis,and wall-shear stress can be used for assessing plaque formations.

Another type of parameter used for functional assessment of coronaryartery stenosis is flow reserve parameters, such as coronary flowreserve (CFR) and fractional flow reserve (FFR). CFR is defined as theratio of maximal hyperemic flow in a coronary to the flow in the samecoronary at rest. FFR is defined as the ratio of the maximal blood flowin the stenotic vessel to the maximal blood flow in a normal vessel, andis used to characterize the severity of stenosis. In clinical practice,pressure/flow based measurements are used to determine these flowreserves. Accordingly, according to an embodiment of the presentinvention, the method of claim 1 can be used to estimate these flowreserves.

According to an embodiment of the present invention, medical image data,such as high resolution CT data, can be used for anatomic modeling ofthe coronary, and for determining the maximum velocity based on contrastmedium propagation. This is subsequently used for performingpatient-specific CFD analysis, the results of which are used in afitting procedure that maps the maximum velocity to an average velocityin order to determine the flow rates necessary for calculating CFRvalues.

FIG. 4 illustrates a method of non-invasive assessment of coronary flowreserve based on medical image data according to an embodiment of thepresent invention. As illustrated in FIG. 4, at step 402, medical imagedata is received for rest and hyperemia. In particular, a first sequenceof image data that is acquired during rest is received and a secondsequence of image data that is acquired during maximal hyperemic flowcondition is received. These sequences of image data can be a sequencesof 3D images (volumes) acquired over a certain time period. Thesequences of image data can be acquired using various medical imagingmodalities. For example, according to various embodiments of the presentinvention, sequences of 3D CT data, 2D dynamic angiography data, and/orrotational angiography data can be received, but the present inventionis not limited thereto. The image data can be received directly from oneor more image acquisition devices, such as a CT scanner or an X-raydevice. It is also possible that previously stored image data be loaded,for example from a memory or storage of a computer system or some othercomputer readable storage medium. The sequences of medical images canshow the propagation of a contrast agent through the coronary arteries.

At step 404, an anatomic model of coronary arteries of interest isgenerated for each of the received image sequences. It is to beunderstood that step 404 can be implemented similarly to step 104 ofFIG. 1, as described above. At step 406, the maximum velocity isestimated for both the rest image data and the hyperemia image databased on contrast agent propagation. In particular, the maximum velocityfor each sequence of image data can be estimated using a spatio-temporalrepresentation of the contrast agent propagation, as described above inconnection with step 106 of FIG. 1.

At step 406, the maximum velocity at rest is mapped to an average restvelocity and a maximum velocity at hyperemia is mapped to an averagehyperemia velocity using patient-specific CFD simulations. FIG. 5illustrates determination of flow rate in a vessel from a velocityprofile of the blood in the vessel. As illustrated in FIG. 5, for anaccurate assessment of blood flow rate in a given vessel 500, velocityinformation u is needed on the entire cross-section S of the vessel 500.The blood flow rate Q can be determined by integrating the flow profileρu (where ρ is the density the blood) over the surface area S.Accordingly, as illustrated in FIG. 5, the mass flow rate Q can also bedetermined as Q=ρAU , where U is the average blood velocity and A is thearea of the cross-section S . Non-invasive blood velocity measurementsrecord the maximum velocity V_(max) on a given cross-section, therebyrequiring assumptions on the velocity profile to determine the bloodflow rate. In some cases, the flow rate is determined from the maximumvelocity value by assuming a parabolic velocity profile. According tothis criterion, the average velocity is determined as 0.5 V_(max).However, this assumption does not take into account patient-specificgeometry and hemodynamics.

Instead of making assumptions regarding the velocity profile of avessel, CFD simulations can be used to obtain a more realistic relationmapping the maximum velocity V_(max) to the average velocity V_(avg).For small vessels, including coronary arteries, the following relationis used to map V_(max) to V_(avg):

$\begin{matrix}{{V_{avg} = {{f\left( {V_{\max},W} \right)} = {V_{\max}\frac{\left( {1 + {p\; W^{q}}} \right)}{2}}}},} & (1)\end{matrix}$where W is the Womersley number, defined as

${W = {R\sqrt{\frac{f\;\rho}{\mu}}}},$where f is the frequency of the pulsatile flow, R is the characteristiclength scale (cross-sectional area of the coronary), ρ is the density,and μ the dynamic viscosity of blood.

The parameters p and q are determined using a fitting procedure, whichuses data from a series of CFD simulations performed under defectiveboundary conditions, where instead of prescribing velocity profileboundary conditions, only flow values are specified. In particular, aseries of CFD simulations are performed in which different flow ratesare specified and the values for parameters such as W, f, R, ρ, and/or μare varied. Each simulation results in a value for V_(max) and a valuefor V_(avg). Based on the values used for each simulation and theresulting values for V_(max) and V_(avg), the mapping parameters p and qare determined by fitting these parameters to the data resulting fromthe simulations. For example, these parameters may be fit to the datausing a non-linear least squares fitting algorithm.

Once the mapping parameters p and q are determined based on the CFDsimulations, the maximum velocity V_(max) determined in step 404 can bemapped to an average velocity V_(avg) using the Womersley number and themapping parameters, as shown in Equation (1). This is performedseparately for the rest image data and the hyperemia image data,resulting in an average rest blood velocity and an average hyperemiablood velocity.

At step 408, the CFR is calculated based on the average rest bloodvelocity and the average hyperemia blood velocity. In particular, theCFR can be calculated as:

$\begin{matrix}{{{CFR} = {\frac{Q_{hyp}}{Q_{rest}} = \frac{\rho\; A_{hyp}V_{hyp}}{\rho\; A_{rest}V_{rest}}}},} & (2)\end{matrix}$where V_(hyp) and V_(rest) are the average velocity values derived from

${V_{avg} = {V_{\max}\frac{\left( {1 + {p\; W^{q}}} \right)}{2}}},$and A_(hyp) and A_(rest), are the cross-sectional areas of the coronaryartery at hyperemia and at rest, respectively.

In the absence of the second sequence of medical images (i.e. imagesacquired during hyperemia), a similar method as presented above in FIG.4, can still be applied. In such a case, the hyperemic blood flowanalysis can be performed by using a different set of outlet boundaryconditions (i.e. the boundary conditions modeling the flowcharacteristics of the coronary bed). Since most of the resistance tothe flow in the coronaries is present in the microvascular circulation,the hyperemia condition is simulated by appropriately changing theresistance/impedance values in the outlet boundary conditions.Additional details on the resistance/impedance values appropriate tosimulate the hyperemia condition are described in S. Mantero, et al.,“The Coronary Bed and its Role in the Cardiovascular System: A Reviewand an Introductory Single-Branch Model”, Journal of BiomedicalEngineering, Volume 14, Issue 2, March 1992, Pages 109-116.

The above-described methods for non-invasive assessment of coronaryartery disease may be implemented on a computer using well-knowncomputer processors, memory units, storage devices, computer software,and other components. A high-level block diagram of such a computer isillustrated in FIG. 6. Computer 602 contains a processor 604, whichcontrols the overall operation of the computer 602 by executing computerprogram instructions which define such operation. The computer programinstructions may be stored in a storage device 612 (e.g., magnetic disk)and loaded into memory 610 when execution of the computer programinstructions is desired. Thus, the steps of the methods of FIGS. 1 and 4may be defined by the computer program instructions stored in the memory610 and/or storage 612 and controlled by the processor 604 executing thecomputer program instructions. An image acquisition device 620, such asa CT scanning device, X-ray acquisition device, etc., can be connectedto the computer 602 to input image data to the computer 602. It ispossible to implement the image acquisition device 620 and the computer602 as one device. It is also possible that the image acquisition device620 and the computer 602 communicate wirelessly through a network. Thecomputer 602 also includes one or more network interfaces 606 forcommunicating with other devices via a network. The computer 602 alsoincludes other input/output devices 608 that enable user interactionwith the computer 602 (e.g., display, keyboard, mouse, speakers,buttons, etc.). Such input/output devices 608 may be used in conjunctionwith a set of computer programs as an annotation tool to annotatevolumes received from the image acquisition device 620. One skilled inthe art will recognize that an implementation of an actual computercould contain other components as well, and that FIG. 6 is a high levelrepresentation of some of the components of such a computer forillustrative purposes.

The foregoing Detailed Description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the invention disclosed herein is not to be determined from theDetailed Description, but rather from the claims as interpretedaccording to the full breadth permitted by the patent laws. It is to beunderstood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that variousmodifications may be implemented by those skilled in the art withoutdeparting from the scope and spirit of the invention. Those skilled inthe art could implement various other feature combinations withoutdeparting from the scope and spirit of the invention.

The invention claimed is:
 1. A method of non-invasive assessmentcoronary flow reserve (CFR) using medical image data, comprising:receiving a first sequence of medical image data acquired during aresting state using a computed tomography (CT) scanner or an X-ray imageacquisition device and a second sequence of medical image data acquiredduring hyperemia using a computed tomography (CT) scanner or an X-rayimage acquisition device; generating a first anatomical model of acoronary artery from the first sequence of medical image data and asecond anatomical model of the coronary artery from the second sequenceof medical image data; estimating a maximum velocity of blood on across-section of the coronary artery during the resting state based on aspatio-temporal representation of contrast agent propagation over alength of the coronary artery in the first sequence of medical imagedata and estimating a maximum velocity of blood on the cross-section ofthe coronary artery during hyperemia based on a spatio-temporalrepresentation of contrast agent propagation over the length of thecoronary artery in the second sequence of medical image data; mappingthe maximum velocity of the blood on the cross-section of the coronaryartery during the resting state to an average rest velocity representinga spatial average of a velocity profile over the cross-section of thecoronary artery during the resting state using patient-specific mappingparameters, and mapping the maximum velocity of the blood on thecross-section of the coronary artery during hyperemia to an averagehyperemia velocity representing a spatial average of a velocity profileover the cross-section of the coronary artery during hyperemia usingpatient-specific mapping parameters; and calculating the coronary flowreserve for the coronary artery based on the average rest velocity andthe average hyperemia velocity.
 2. The method of claim 1, wherein thestep of estimating a maximum velocity of blood on a cross-section of thecoronary artery during the resting state based on a spatio-temporalrepresentation of contrast agent propagation over a length of thecoronary artery in the first sequence of medical image data andestimating a maximum velocity of blood on the cross-section of thecoronary artery during hyperemia based on a spatio-temporalrepresentation of contrast agent propagation over the length of thecoronary artery in the second sequence of medical image data comprises,for each of the first and second sequences of medical image data:generating the spatio-temporal representation of contrast agentpropagation based on time-intensity curves extracted from the respectivesequence of medical image data; and estimating a slope of thespatio-temporal representation of contrast agent propagation.
 3. Themethod of claim 2, wherein the step of generating the spatio-temporalrepresentation of contrast agent propagation based on time-intensitycurves extracted from the respective sequence of medical image datacomprises: mapping an inverted intensity magnitude of points in therespective sequence of medical image data over the length of thecoronary artery over time.
 4. The method of claim 1, wherein the step ofmapping the maximum velocity of the blood on the cross-section of thecoronary artery during the resting state to an average rest velocityrepresenting a spatial average of a velocity profile over thecross-section of the coronary artery during the resting state usingpatient-specific mapping parameters, and mapping the maximum velocity ofthe blood on the cross-section of the coronary artery during hyperemiato an average hyperemia velocity representing a spatial average of avelocity profile over the cross-section of the coronary artery duringhyperemia using the patient-specific mapping parameters comprises:mapping the maximum velocity during the resting state to the averagerest velocity and the maximum velocity during hyperemia to the averagehyperemia velocity based on a Womersley number based procedure and thepatient-specific mapping parameters.
 5. The method of claim 1, whereinthe step of mapping the velocity of the blood on the cross-section ofthe coronary artery during the resting state to an average rest velocityrepresenting a spatial average of a velocity profile over thecross-section of the coronary artery during the resting state usingpatient-specific mapping parameters, and mapping the maximum velocity ofthe blood on the cross-section of the coronary artery during hyperemiato an average hyperemia velocity representing a spatial average of avelocity profile over the cross-section of the coronary artery duringhyperemia using patient-specific mapping parameters comprises, for eachof the maximum velocity during the resting state and the maximumvelocity during hyperemia: mapping a maximum velocity to an averagevelocity as${V_{avg} = {V_{\max}\frac{\left( {1 + {p\; W^{q}}} \right)}{2}}},$ where V_(max) is the maximum velocity, V_(avg) is the average velocity,W is the Womersley number, defined as${W = {R\sqrt{\frac{f\;\rho}{\mu}}}},$  where f is a frequency of apulsatile flow, R is a cross-sectional area of the coronary artery, ρ isthe density of blood, and μ the dynamic viscosity of blood, and p and qare the patient-specific mapping parameters determined using a series ofcomputational fluid dynamics (CFD) simulations.
 6. The method of claim5, wherein the step of mapping a maximum velocity to an average velocityfurther comprises: performing a series of computational fluid dynamics(CFD) simulations on the respective anatomical model of the coronaryartery having various prescribed flow values and varying values for atleast one of W, f, R, ρ, or μ, resulting in various simulated values forthe maximum velocity and the average velocity; and determining valuesfor the patient-specific mapping parameters p and q by fitting themapping parameters to the simulated values for the maximum velocity andthe average velocity.
 7. The method of claim 1, wherein the step ofcalculating the coronary flow reserve for the coronary artery based onthe average rest velocity and the average hyperemia velocity comprises:calculating the coronary flow reserve (CFR) as${{CFR} = \frac{\rho\; A_{hyp}V_{hyp}}{\rho\; A_{rest}V_{rest}}},$ where V_(hyp) is the average hyperemia velocity, V_(rest) is theaverage rest velocity, p is the density of blood, A_(hyp) is thecross-sectional area of the second anatomical model, and A_(rest) is thecross-sectional area of the first anatomical model.
 8. An apparatus fornon-invasive assessment coronary flow reserve (CFR) using medical imagedata, comprising: a processor; and a memory storing computer programinstructions, which when executed by the processor cause the processorto perform operations comprising: receiving a first sequence of medicalimage data acquired during a resting state using a computed tomography(CT) scanner or an X-ray image acquisition device and a second sequenceof medical image data acquired during hyperemia using a computedtomography (CT) scanner or an X-ray image acquisition device; generatinga first anatomical model of a coronary artery from the first sequence ofmedical image data and a second anatomical model of the coronary arteryfrom the second sequence of medical image data; estimating a maximumvelocity of blood on a cross-section of the coronary artery during theresting state based on a spatio-temporal representation of contrastagent propagation over a length of the coronary artery in the firstsequence of medical image data and estimating a maximum velocity ofblood on the cross-section of the coronary artery during hyperemia basedon a spatio-temporal representation of contrast agent propagation overthe length of the coronary artery in the second sequence of medicalimage data; mapping the maximum velocity of the blood on thecross-section of the coronary artery during the resting state to anaverage rest velocity representing a spatial average of a velocityprofile over the cross-section of the coronary artery during the restingstate using patient-specific mapping parameters and mapping the maximumvelocity of the blood on the cross-section of the coronary artery duringhyperemia to an average hyperemia velocity representing a spatialaverage of a velocity profile over the cross-section of the coronaryartery during hyperemia using patient-specific mapping parameters; andcalculating the coronary flow reserve for the coronary artery based onthe average rest velocity and the average hyperemia velocity.
 9. Theapparatus of claim 8, wherein estimating a maximum velocity of blood ona cross-section of the coronary artery during the resting state based ona spatio-temporal representation of contrast agent propagation over alength of the coronary artery in the first sequence of medical imagedata and estimating a maximum velocity of blood on the cross-section ofthe coronary artery during hyperemia based on a spatio-temporalrepresentation of contrast agent propagation over the length of thecoronary artery in the second sequence of medical image data comprises:generating a spatio-temporal representation of contrast agentpropagation based on time-intensity curves extracted from a sequence ofmedical image data; and estimating a slope of the spatio-temporalrepresentation of contrast agent propagation.
 10. The apparatus of claim9, wherein generating the spatio-temporal representation of contrastagent propagation based on time-intensity curves extracted from asequence of medical image data comprises: mapping an inverted intensitymagnitude of points in the respective sequence of medical image dataover the length of the coronary artery over time.
 11. The apparatus ofclaim 8, wherein mapping the velocity of the blood on the cross-sectionof the coronary artery during the resting state to an average restvelocity representing a spatial average of a velocity profile over thecross-section of the coronary artery during the resting state usingpatient-specific mapping parameters and mapping the maximum velocity ofthe blood on the cross-section of the coronary artery during hyperemiato an average hyperemia velocity representing a spatial average of avelocity profile over the cross-section of the coronary artery duringhyperemia using patient-specific mapping parameters comprises: mapping amaximum velocity to an average velocity as${V_{avg} = {V_{\max}\frac{\left( {1 + {p\; W^{q}}} \right)}{2}}},$ where V_(max) is the maximum velocity, V_(avg) is the average velocity,W is the Womersley number, defined as${W = {R\sqrt{\frac{f\;\rho}{\mu}}}},$  where f is a frequency of apulsatile flow, R is a cross-sectional area of the coronary artery, ρ isthe density of blood, and μ the dynamic viscosity of blood, and p and qare the patient-specific mapping parameters determined using a series ofcomputational fluid dynamics (CFD) simulations.
 12. The apparatus ofclaim 11, wherein mapping a maximum velocity to an average velocityfurther comprises: performing a series of computational fluid dynamics(CFD) simulations on the respective anatomical model of the coronaryartery having various prescribed flow values and varying values for atleast one of W, f, R, ρ, and/or μ, resulting in various simulated valuesfor the maximum velocity and the average velocity; and determiningvalues for the patient-specific mapping parameters p and q by fittingthe mapping parameters to the simulated values for the maximum velocityand the average velocity.
 13. The apparatus of claim 8, whereincalculating the coronary flow reserve for the coronary artery based onthe average rest velocity and the average hyperemia velocity comprises:means for calculating the coronary flow reserve (CFR) as${{CFR} = \frac{\rho\; A_{hyp}V_{hyp}}{\rho\; A_{rest}V_{rest}}},$ where v_(hyp) is the average hyperemia velocity, v_(rest) is theaverage rest velocity, p is the density of blood, A_(hyp) is thecross-sectional area of the second anatomical model, and A_(rest) is thecross-sectional area of the first anatomical model.
 14. A non-transitorycomputer readable medium comprising computer executable instructions forperforming non-invasive assessment coronary flow reserve (CFR) usingmedical image data, the computer executable instructions performingsteps comprising: receiving a first sequence of medical image dataacquired during a resting state using a computed tomography (CT) scanneror an X-ray image acquisition device and a second sequence of medicalimage data acquired during hyperemia using a computed tomography (CT)scanner or an X-ray image acquisition device; generating a firstanatomical model of a coronary artery from the first sequence of medicalimage data and a second anatomical model of the coronary artery from thesecond sequence of medical image data; estimating a maximum velocity ofblood on a cross-section of the coronary artery during the resting statebased on a spatio-temporal representation of contrast agent propagationover a length of the coronary artery in the first sequence of medicalimage data and estimating a maximum velocity of blood on thecross-section of the coronary artery during hyperemia based on aspatio-temporal representation of contrast agent propagation over thelength of the coronary artery in the second sequence of medical imagedata; mapping the maximum velocity of the blood on the cross-section ofthe coronary artery during the resting state to an average rest velocityrepresenting a spatial average of a velocity profile over thecross-section of the coronary artery during the resting state usingpatient-specific mapping parameters, and mapping the maximum velocity ofthe blood on the cross-section of the coronary artery during hyperemiato an average hyperemia velocity representing a spatial average of avelocity profile over the cross-section of the coronary artery duringhyperemia using patient-specific mapping parameters; and calculating thecoronary flow reserve for the coronary artery based on the average restvelocity and the average hyperemia velocity.
 15. The non-transitorycomputer readable medium of claim 14, wherein the computer executableinstructions defining the step of estimating a maximum velocity of bloodon a cross-section of the coronary artery during the resting state basedon a spatio-temporal representation of contrast agent propagation over alength of the coronary artery in the first sequence of medical imagedata and estimating a maximum velocity of blood on the cross-section ofthe coronary artery during hyperemia based on a spatio-temporalrepresentation of contrast agent propagation over the length of thecoronary artery in the second sequence of medical image data comprisecomputer executable instructions defining, for each of the first andsecond sequences of medical image data, the steps of: generating thespatio-temporal representation of contrast agent propagation based ontime-intensity curves extracted from the respective sequence of medicalimage data; and estimating a slope of the spatio-temporal representationof contrast agent propagation.
 16. The non-transitory computer readablemedium of claim 15, wherein the computer executable instructionsdefining the step of generating the spatio-temporal representation ofcontrast agent propagation based on time-intensity curves extracted fromthe respective sequence of medical image data comprise computerexecutable instructions defining the step of: mapping an invertedintensity magnitude of points in the respective sequence of medicalimage data over the length of the coronary artery over time.
 17. Thenon-transitory computer readable medium of claim 14, wherein thecomputer executable instructions defining the step of mapping thevelocity of the blood on the cross-section of the coronary artery duringthe resting state to an average rest velocity representing a spatialaverage of a velocity profile over the cross-section of the coronaryartery during the resting state using patient-specific mappingparameters, and mapping the maximum velocity of the blood on thecross-section of the coronary artery during hyperemia to an averagehyperemia velocity representing a spatial average of a velocity profileover the cross-section of the coronary artery during hyperemia usingpatient-specific mapping parameters comprise computer executableinstructions defining, for each of the maximum velocity at rest and themaximum velocity at hyperemia, the step of: mapping a maximum velocityto an average velocity as${V_{avg} = {V_{\max}\frac{\left( {1 + {p\; W^{q}}} \right)}{2}}},$ where V_(max) is the maximum velocity, V_(avg) is the average velocity,W is the Womersley number, defined as${W = {R\sqrt{\frac{f\;\rho}{\mu}}}},$  where f is a frequency of apulsatile flow, R is a cross-sectional area of the coronary artery, ρ isthe density of blood, and μ the dynamic viscosity of blood, and p and qare the patient-specific mapping parameters determined using a series ofcomputational fluid dynamics (CFD) simulations.
 18. The non-transitorycomputer readable medium of claim 17, wherein the computer executableinstructions defining the step of mapping a maximum velocity to anaverage velocity further comprise computer executable instructionsdefining the steps of: performing a series of computational fluiddynamics (CFD) simulations on the respective anatomical model of thecoronary artery having various prescribed flow values and varying valuesfor at least one of W, f, R, ρ, and/or μ, resulting in various simulatedvalues for the maximum velocity and the average velocity; anddetermining values for the patient-specific mapping parameters p and qby fitting the mapping parameters to the simulated values for themaximum velocity and the average velocity.
 19. The non-transitorycomputer readable medium of claim 14, wherein the computer executableinstructions defining the step of calculating the coronary flow reservefor the coronary artery based on the average rest velocity and theaverage hyperemia velocity comprise computer executable instructionsdefining the step of: calculating the coronary flow reserve (CFR) as${{CFR} = \frac{\rho\; A_{hyp}V_{hyp}}{\rho\; A_{rest}V_{rest}}},$ where V_(hyp) is the average hyperemia velocity, V_(rest) is theaverage rest velocity, p is the density of blood, A_(hyp) is thecross-sectional area of the second anatomical model, and A_(rest) is thecross-sectional area of the first anatomical model.